Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I

Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser (Autoren)

Buch | Softcover

68 Seiten

2023 | 1st ed. 2023
Springer Verlag, Singapore
978-981-19-4644-8 (ISBN)

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The book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular category is not semisimple, topological field theory appears to suggest that mapping class groups do not only act on the spaces of chiral conformal blocks, which arise from the homomorphism functors in the category, but also act on the spaces that arise from the corresponding derived functors. It is natural to ask whether this is indeed the case. The book carefully approaches this question by first providing a detailed introduction to surfaces and their mapping class groups. Thereafter, it explains how representations of these groups are constructed in topological field theory, using an approach via nets and ribbon graphs. These tools are then used to show that the mapping class groups indeed act on the so-called derived block spaces. Toward the end, the book explains the relation to Hochschild cohomology of Hopf algebras and the modular group.

Mapping class groups.- Tensor categories.- Derived functors.

Erscheinungsdatum	29.07.2023
Reihe/Serie	SpringerBriefs in Mathematical Physics ; 44
Zusatzinfo	14 Illustrations, color; 2 Illustrations, black and white; IX, 68 p. 16 illus., 14 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
ISBN-10	981-19-4644-2 / 9811946442
ISBN-13	978-981-19-4644-8 / 9789811946448
Zustand	Neuware